My problem is related to developing empirical formula from the computer simulation results.

I am doing a research on concealed sprinkler to test how long it will activate given a certain range of temperature and velocity in the environment. They are denoted as (U=velocity, T=temperature in Kelvin)

The various sprinkler head has a range of dimensions for the recess housing. These dimensions are measured as vertical and horizontal distance denoted as (A=horizontal, B=vertical).

I ran a CFD simulation using above inputs and obtained convection coefficient (h in W/m^2.K). Convection coefficient is telling us how much heat absorbed from the surrounding environment with certain velocity and temperature values.

So, I have a list of parameters to solve in order to get an empirical formula.

I know there are some relationships with all the parameters. h is the value that I need to find out. The rest of the parameters are known. I have tried dimensional analysis and simple linear regression method. But, both led me no way. Would you be kind to point out how to solve this or recommended me to read some useful reference. Thank you.